Coexistence of lazy frogs on ℤ

Mark Holmes; Daniel Kious

doi:10.1017/jpr.2021.86

Coexistence of lazy frogs on ℤ

Mark Holmes, Daniel Kious

University of Melbourne

Research output: Contribution to journal › Article › peer-review

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Abstract

We study the so-called frog model on with two types of lazy frogs, with parameters respectively, and a finite expected number of dormant frogs per site. We show that for any such and there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.

Original language	English
Pages (from-to)	702-713
Number of pages	12
Journal	Journal of Applied Probability
Volume	59
Issue number	3
Early online date	28 Jun 2022
DOIs	https://doi.org/10.1017/jpr.2021.86
Publication status	Published - 28 Sept 2022

Bibliographical note

Funding Information:
The work of Holmes is supported by Future Fellowship FT160100166 from the Australian Research Council.

Keywords

Frog model
coexistence
competing growth
random walk

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1017/jpr.2021.86

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This article has been published in Journal of Applied Probability http://doi.org/10.1017/jpr.2021.86. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © The Authors, 2022.
Accepted author manuscript, 1.38 MBLicence: CC BY-NC-ND

Cite this

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Coexistence of lazy frogs on ℤ

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Random walks in dynamic random environment

Cite this

Coexistence of lazy frogs on ℤ

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Random walks in dynamic random environment

Cite this